1. Field of Invention
This invention pertains to techniques for determining characteristics of earth formations and, more particularly, to techniques to determine water saturation in laminated shale-sand formations from measurements of resistivity anisotropy.
2. Related Art
Electrical anisotropy has been used to detect low-resistivity, low-contrast pay zones such as can occur in thin-bed formations. A water-wet formation with large variability in grain size can be highly anisotropic in the oil-bearing portion and isotropic in the water-bearing portion. The resistivity anisotropy is generally attributed to grain-size variations that affect irreducible water saturation between the laminations. Thin, interbedded sandstones, siltstones, and mudstones have been modeled in which the models contain, for example, layers of low-permeability mudstone and layers of permeable sandstone with variable clay content. The simulated resistivity data are generally described as either perpendicular resistivity, meaning measured with current flowing perpendicular to the bedding, or parallel resistivity, meaning measured with current flowing parallel to the bedding. Plotting perpendicular resistivity versus parallel resistivity for a given interval provides an indication of how hydrocarbon saturation influences electric anisotropy (see FIG. 1).
An algorithm to compute water saturation in thin-bedded formations has been suggested in which the inputs include the horizontal resistivity, the vertical resistivity, the fine-grained volumetric fraction, and the water resistivity. In this approach, the thin bed is considered to be a bi-modal system having both coarse grain layers and fine grain layers. Knowing the horizontal and vertical resistivity and the amount of fine-grain material (from NMR measurement, for example), one can calculate the resistivity of the coarse grain and fine grain layers. One can then calculate the amount of water in each layer using, for example, Archie's law (with m and n equal to 2), and then the total amount of water and oil in the system by volumetric computation. This algorithm is summarized in FIG. 2. Again, this model assumes the system is a dual system (coarse grain and fine grain), the fraction of each material is known, the average porosity for the two layer types is equal, and the water resistivity is known.
A limitation of those two approaches is that they assume each layer is individually isotropic (i.e., Rv and Rh are equal in each layer). Recent log data acquired in laminated shale-sand formations indicate that in fact shale can be anisotropic.